Our changing views of the infinite!
While looking at the world around us, we cannot miss the harmony and order that meets our eye and refines our perception. Yet, when human mind has tried to understand what holds the nature together, it has faced defeat in putting the concept into easy bits of understanding.
Take for instance a simple trajectory formed by a ball when tossed from hand to another. We could see that the movement is definitive and we have a reflex to move and catch it at the frail end of the trajectory. We try to model this information into a logical equation - what we simply call as the motion. To understand it accurately, we break the path down into smaller parts and try to define coordinates from one path point to another. This process can be carried out infinite times, to break the path into infinitesimally ( ΔX ) smaller parts that would add most accurately to the final path, which to us would be the most definitive description of the motion.
To our simplified perception, ∑( ΔX ) = X, and we complete the trajectory by successfully predicting the trajectory and catching the ball.
How easily have we built our understanding on the use of the infinite! Wait for a moment, and think about it. we have broken the path down to "infinite" parts and then simply added these "infinite" parts to define our concept. It is this infinite, that has for centuries built a base for us to build smallest and the largest concepts.
The question remains of how well do we understand the "infinite": ∞.
There have been attempts to unravel the infinite, take the circle for instance, you could fit a triangle, at the next level, quadrilateral, further a pentagon and keep increasing the equal sided polygons. What you would end up is an infinite sided polygon would be a perfect circle! Taking the concept further, if you were to draw lines from the center of the polygon to each vertex, then, you would have the entire area of the circle filled with lines. But, if we stretch our imagination a little further, and observe carefully, we would see that there would be still gaps between one vertex and another! Which would mean that after painfully building the infinite-sided polygon, we are unable to get a perfect circle!
This indeeds distorts our view that circle is perfectly rounded and leaves us with an indefinite view of what circle would look like. World it seems is not a perfection of order and harmony.
This disruption in order and perfection, because of the lack of understanding of the infinite has disturbed the normative characteristics of definite, the base of mathematics. It is true that one cannot build an edifice on thin air, thus, great works of mathematics could not be built on a limited knowledge of the infinite (which ironically is the building block of mathematics).
It was in such times that
Georg Cantor built his famous theory that shook the world by bringing the infinite into the realms of arithmetics of infinite, thus destroying the definite view of concepts. This work was further carried out by
Ludwig Boltzmann, who gave the final blow to the order and harmony by his revolutionary work in thermodynamics. He picked up from where Cantor left, suggesting that order and harmony is based not on the definite events but on the random collisions of atoms within the matter! While world understood events as symmetrical on time axis ( that is you could reverse an event and arrive back on the initial situation), entropy changed that viewpoint and brought decay into the heart of physics. Boltzmann went further to show probabilistic dependency of entropy, S=k.log(W) thus making the change irreversible. This proved that in what see as order, there remains an element of uncertainty at its core.
Thus, we have to believe that world after all is not definite! There is a chaos and randomness which is the pure essence of existence.
Indeed, randomness is our new constant!
